LEESBURG, Va. (Reuters) - U.S. House of Representatives Democrats are accusing Republican President Donald Trump of aggravating a crisis situation at the southern U.S. border, saying he has not used funds available to help deal with a surge of migrants and exacerbated the problem with his attempts to crack down.

House Speaker Nancy Pelosi said Thursday that bipartisan immigration reform, which has eluded Congress and the White House for years, is still the solution. It is in fact "inevitable," Pelosi said on the sidelines of a Democratic party meeting in Leesburg, Virginia.

In Washington, Senate Majority Leader Mitch McConnell, a Republican, also called for bipartisan discussions on immigration. But he focused on toughening U.S. asylum law, a move that Democrats likely would oppose.

Democrats have not proposed a comprehensive immigration bill since taking the majority in the House this year. Republicans still hold the Senate.

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Instead, Democrats last month proposed legislation offering a pathway to citizenship for more than 2 million undocumented immigrants who were brought illegally to the United States as children. Known as Dreamers, they face possible deportation.

The House Democratic bill would also help immigrants from countries hit by civil conflicts or natural disasters who have temporary protected status, known as TPS.

U.S. officers arrested or denied entry to over 103,000 people along the border with Mexico in March, a 35 percent increase over the prior month and more than twice as many as the same period last year, according to data released by U.S. Customs and Border Protection this week.

The steady increase in migrant arrivals, which has been building over the past several months, is driven by a growing number of children and families, especially from Central America.

Trump has threatened to close the border, saying the United States is "full." He has urged the building of a wall on the southern border since before he became president in 2016. Recently his ire has been directed at his own officials, Congress, and Latin American countries, who he says have not done enough to stop their citizens from traveling to the United States.

Pelosi, asked Thursday what should be done at the border, said the bipartisan legislation Trump signed to end a government shutdown in February included money for judges and humanitarian aid "to bring order to the border," but Trump has not used the funds.

Although a bipartisan effort at comprehensive immigration reform by Democrats and Trump last year failed, Pelosi said such an overhaul still had a chance.

"I'm not giving up on the president on this," Pelosi said. "I still say to him, 'We've got to have comprehensive immigration reform'."

Representative Pramila Jayapal, speaking to reporters later, said the Trump administration had manufactured a crisis at the border in part by "stripping away" legal routes to immigration, such as by stopping asylum seekers at legal ports of entry.

Trying to curb the flow of Central American asylum seekers, the administration has been sending more people back to Mexico to wait for their asylum claims to be heard by U.S. courts.

Representative David Cicilline said the Trump administration had exacerbated a challenging border situation by not spending money that was appropriated for border facilities and personnel, as well as by cutting off aid to Central American countries for sending migrants to the United States.

Cicilline, who runs the House Democrats' policy and communications committee, denied Democrats were simply "looking on helplessly" at the problems.

"But the administration has responsibility in all these areas. And we can appropriate funding and we can pass legislation but ultimately they are responsible for executing the immigration laws in this country," he said.